• Placement Questions

Placement Papers with Solutions

(#M40009195) SELF QUESTION Keep an EYE

f I drive half-way to the city at 30 km/hour, how fast do I have to go for the rest of the way to make the average speed for the entire journey of 60 km/hour?

Flower (13 years ago)

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(#M40009194) SELF QUESTION Keep an EYE

An eccentric professor used a unique way to measure time for a test lasting 15 minutes.

He used just two hourglasses. One measured 7 minutes and the other 11 minutes.

During the whole time he turned the hourglasses only 3 times.

How did he measure the 15 minutes?

Flower (13 years ago)

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(#M40009193) SELF QUESTION Keep an EYE

You need to boil eggs for exactly 9 minutes, or else the visiting Duchess will complain, and you will lose your job as head chef.

But you have only 2 Hourglasses, one measures 7-minutes, and the other measures 4-minutes. How can you correctly measure 9 minutes?

Flower (13 years ago)

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(#M40009192) SELF QUESTION Keep an EYE

The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town

The town has now reached its maximum population - what is it?

Flower (13 years ago)

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(#M40009191) SELF QUESTION Keep an EYE

You have to do an experiment to determine the highest floor on a 100-floor building from which a manufactured snooker ball may be dropped without breaking.

You are given two identical snooker balls, which you can drop from various floors of the building, to carry out your experiment.

If a ball doesn't break after being dropped, it may be reused without suffering any loss of quality. But if both balls break before you have determined the highest floor, then you are an incompetent bungler and your boss is ultimately going to fire you.

What is the least number of times you must drop the snooker balls in order to determine the highest floor?

Flower (13 years ago)

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(#M40009190) SELF QUESTION Keep an EYE

We know very little about the life of the mathematician Diophantus (often known as the 'father of algebra') except that he came from Alexandria and he lived around the year 250 AD.

However, there remains a riddle that describes the spans of Diophantus's life:

"This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life."

In simpler English it says: Diophantus's youth lasted 1/6 of his life. He had the first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.

How long did Diophantus live?

Flower (13 years ago)

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(#M40009189) SELF QUESTION Keep an EYE

Imagine a 3x3x3 cube.

How many cuts do we need to break it into 27 1x1x1 cubes?

A cut may go through multiple pieces.

Flower (13 years ago)

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(#M40009188) SELF QUESTION Keep an EYE

n front of you are several long fuses. You know they burn for exactly one hour after you light them at one end. The entire fuse does not necessarily burn at a constant speed. For example, it might take five minutes to burn through half the fuse and fifty-five minutes to burn the other half.

With your lighter and using these fuses, how can you measure exactly three-quarters of an hour of time?

Flower (13 years ago)

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(#M40009187) SELF QUESTION Keep an EYE

Joey leaves his house in the morning to go to day camp.

Just as he is leaving his house he looks at an analog clock reflected in the mirror.

There are no numbers on the clock, so Joey makes an error in reading the time since it is a mirror image. Joey assumes there is something wrong with the clock and rides his bike to day camp.

He gets there in 20 minutes and finds that just as he gets there the day camp clock has a time that is 2 1/2 hours (2 hours and 30 minutes) later than the time that he saw in the mirror image of his clock at home.

What time was it when he got to day camp?

(The clock at camp and the clock at home were both set to the correct time.)

Flower (13 years ago)

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(#M40009186) SELF QUESTION Keep an EYE

You have six beads placed in a plane.

The object is to find two pairs of equidistant beads. (In other words, find a pair of beads that are exactly the same distance apart as another pair of beads).

The distance between two beads is meant as the distance between their centers.

Flower (13 years ago)

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